Problem: Express your answer as a mixed number simplified to lowest terms. $15\dfrac{1}{10}-7\dfrac{5}{6} = {?}$
Solution: Find a common denominator for the fractions: $= {15\dfrac{3}{30}}-{7\dfrac{25}{30}}$ Convert ${15\dfrac{3}{30}}$ to ${14 + \dfrac{30}{30} + \dfrac{3}{30}}$ So the problem becomes: ${14\dfrac{33}{30}}-{7\dfrac{25}{30}}$ Separate the whole numbers from the fractional parts: $= {14} + {\dfrac{33}{30}} - {7} - {\dfrac{25}{30}}$ Bring the whole numbers together and the fractions together: $= {14} - {7} + {\dfrac{33}{30}} - {\dfrac{25}{30}}$ Subtract the whole numbers: $=7 + {\dfrac{33}{30}} - {\dfrac{25}{30}}$ Subtract the fractions: $= 7+\dfrac{8}{30}$ Combine the whole and fractional parts into a mixed number: $= 7\dfrac{8}{30}$ Simplify to lowest terms: $= 7\dfrac{4}{15}$